Compound nested lattices with programmable isotropy and elastic stiffness up to the theoretical limit

Abstract

A novel class of compound structures, which consists of 2 types of unit cell geometries occupying different sites in the lattice (i.e. compound lattice) was investigated. The arrangement and volume ratio of the 2 unit cell geometries were varied, and it was found that the compound lattices can exhibit up to 4 distinct geometries – 2 from the unit cells and 2 supra-structures from the arrangement of each type of unit cell. In stiffness optimization, the material re-organization tends to emphasize the stiffest of the 4 geometries and collapse the hierarchical compound lattice into a single-level structure. In isotropy optimization, unit cells had to be arranged into supra-structures with an anisotropy profile opposite to that of their geometries. These insights led to the introduction of the compound nested lattices, which exhibited higher specific moduli than previous isotropic designs. The compound nested 1pSC:512pFCC lattice, in particular, reached 97.9 % of the Hashin-Shtrikman upper bound at relative density = 0.6, which is the closest approach to the theoretical maximum ever reported.